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QCD Critical Point

QCD Critical Point. Outline: QCD Phase Diagram Experimental Study of QCD Critical Point Conclusions and Outlook. Bedanga Mohanty VECC, Kolkata. ATHIC - 2010, Wuhan, China. Phase Transitions. Physical systems undergo phase transitions when external

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QCD Critical Point

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  1. QCD Critical Point Outline: QCD Phase Diagram Experimental Study of QCD Critical Point Conclusions and Outlook Bedanga Mohanty VECC, Kolkata ATHIC - 2010, Wuhan, China

  2. Phase Transitions Physical systems undergo phase transitions when external parameters such as the temperature (T) or a chemical potential (μ) are tuned. Systems following Quantum Chromodynamics (QCD) - No exception Associated chemical potential Conserved Quantities: Baryon Number ~  Electric Charge ~ Q ~ small Strangeness ~ S ~ small In principle a four dimensional phase diagram A simpler version : T vs. 

  3. Phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically distinct phases QCD Phase Diagram Water : Atomic QCD (Hadrons -- Partons) Theory and Experimental approaches Precisely known 14 APRIL 2006 VOL 312 SCIENCE, Page 190 Establish the phase boundary Find the QCD Critical Point

  4. Order of Phase Transition at B ~ 0 Y. Aoki et al., Nature443:675-678,2006 1st order : Peak height ~ V Peak width ~ 1/V Cross over : Peak height ~ const. Peak width ~ const. 2nd order : Peak height ~ V No significant volume dependence (8 times difference in volumes) Phase transition at high T and B = 0 is a cross over Lattice results on electroweak transition in standard model is an analytic cross-over for large Higgs mass K. Kajantie et al., PRL 77, 2887-2890,2006

  5. First Principle QCD Calculations on Lattice: M : Dirac Matrix SG : Gluonic action Issue for non zero , Det M is not positive definite -- Sign problem Reweighting Taylor Expansion R. Gavai and S. Gupta Phys. Rev. D 78, 14503 (2008) Z. Fodor and S.D. Katz JHEP 0404, 50 (2004) CP exists 1st order transition at large  TE/TC = 0.94 +/- 0.01 E /TE = 1.8 +/- 0.1 TE = 162 +/- 2 MeV E = 360 +/- 40 MeV QCD Critical Point 2nd order point in the PD,where the 1st order transition lines ends

  6. QCD Phase Diagram: Theoretical Lattice and other QCD based models : B = 0 - Cross-over TC ~ 170-195 MeV B > 160 MeV - QCD critical point Experimental Study How to access PD Establish Phase Boundary Locate CP Tc: M. Cheng et al, Phys. Rev. D 74, 054507 (2006) Y. Aoki et al, Phys. Lett. B 643, 46 (2006); 0903.4155

  7. Accessing Phase Diagram Nature 448:302-309,2007 data Tch = 163 ± 4 MeV B = 24 ± 4 MeV RHIC white papers - 2005, Nucl. Phys. A757, STAR: p102; PHENIX: p184. Thermal model fits Varying beam energy varies Temperature and Baryon Chemical Potential

  8. Partonic collectivity No NCQ Scaling  v2 small Chiral Magnetic effect No Dynamical Charge Asymmetry PHENIX : PRL 101, 232301 (2008) Establishing The Phase Boundary Au+Au 200 GeV Jet quenching No Jet Quenching STAR: Phys. Rev. Lett. 99 (2007)112301 STAR: Phys. Rev. Lett. 103 (2009) 251601

  9. Locating The QCD Critical Point In the fields of observation chance favors only the prepared mind. -- Louis Pasteur Strategy: (I) Establish observables for Critical Point which has sound theoretical basis and reflects the signatures at CP. (II) Expectations from the observable from non critical point physics should be understood. (III) Vary beam energy of collisions and look for non-monotonic dependence of the observable.

  10. Signature of Critical Point • Distributions become non Gaussian • Correlation length diverges • Susceptibilities diverges • Long wavelength fluctuations or low momentum fluctuations important T > TC T~TC T < TC Critical Opalescence as observed in CO2 liquid-gas transition T. Andrews. Phil. Trans. Royal Soc., 159:575, 1869

  11. Measure of Non-Gaussian Nature Deviation D: Laplace distribution kurtosis = 3 S: hyperbolic secant distribution kurtosis = 2 L: logistic distribution kurtosis = 1.2 N: normal distribution kurtosis = 0 C: raised cosine distribution kurtosis = −0.59376 W: Wigner semicircle distribution kurtosis = −1 U: uniform distribution kurtosis = −1.2. Standard deviation, s = Kurtosis Skewness Skewness and Kurtosis are measures of non-Gaussian nature of the distribution.

  12. Net-proton Number Fluctuations ~ Singularity in charge and baryon number susceptibilities Distributions non Gaussian at QCP Moments and Correlation length () < (N)2> ~ 2 < (N)3> ~ 4.5 Q = B/2 + I3 < (N)4> - 3 < (N)2>2 ~ 7 Q ~ (1/VT) < (Q)2> = (1/4) B + I ~ (1/VT) < (Np-pbar)2> Value limited in heavy-ion collisions Finite size effects < 6 fm Critical slowing down, finite time effects  ~ 2 - 3 fm iso-spin blindness of  field Higher moments higher sensitivity At QCP Link to Lattice QCD and QCD Models Kurtosis x Variance ~ 4)/ [c T2] Skewness x Sigma ~ [3) T]/ [c T2] R. Gavai & S. Gupta, arXiv:1001.3796 Higher Moments of Net-Protons M. Cheng et al, PRD 79, 074505 (2009) B. Stokic et al, PLB 91, 192 (2009) R. Gavai & S. Gupta PRD 78, 114503 (2008) M. A. Stephanov, PRL 102, 032301 (2009) Y. Hatta et al,PRL 91, 102003 (2003) Non monotonic variation of products of higher moments with beam energy

  13. CP Model (C. Athanasiou,M. Stephanov, K. Rajagopal, arXiv:1006.4636 andPRL 102 (2009) 032301) Theory Expectations Lattice QCD (R. Gavai, S. Gupta, arXiv:1001.3796) Beam Energy (GeV) Kurtosis x Variance (net protons) with  ~ 3fm and CP (No CP ~ 1) 200 ~ 2.5 62 ~ 35 19 ~ 3700 7.7 ~ 29600 KurtosisxVariance QCP m2 equivalent to Kurtosis x Variance At CP : Systems falls out of equilibrium will lead to deviations from Lattice QCD √s

  14. Beam energy Collision centrality Observable and Non-CP Physics Au+Au 200 GeV mid-rapidity, pT : 0.4-0.8 GeV/c • Kurtosis x Variance: (Desirable features for CP Search) • Constant as a function of beam energy • Constant as a function of collision centrality/impact parameter • No difference between net-baryon and net-proton • Effect of resonance decay small • Similar values for Transport, Mini-jets, Coalescence models • Unity for Thermal model

  15. Data: Net-Proton Distribution Clean identification of protons in STAR TPC for the transverse momentum range : 0.2 - 1 GeV/c. All results for Au+Au collisions at 19.6, 62.4 and 200 GeV collisions STAR: PRL 105 (2010) 022302

  16. STAR: PRL 105 (2010) 022302 Moments: Net-Proton Distribution Moments: Central Limit Theorem: Mi = CMx <Npart>I 2i = C 2x <Npart>I Si = Sx/√[C <Npart>]I i = x/[C <Npart>]I Consistent with CLT expectations (lines) Moments (~ baryon number susceptibilities) do not change with system volume -- Typical feature for crossover

  17. STAR: PRL 105 (2010) 022302 Data and Lattice QCD S  ~   Assumptions: Net-proton ~ net-Baryon Thermalization Modelling: Chemical Freeze-out Good agreement with Lattice QCD R. Gavai & S. Gupta arXiv:1001.3796

  18. Energy Dependence STAR: PRL 105 (2010) 022302 CP Model: 2 > 2 arXiv: 1006.4636; PRL 102 (2009) 032301 Models: CB ~ 100 MeV PRL 101 (2008) 122302; PLB 647 (2007) 431 Eur. Phys. Lett. 86 (2009) 31001 Observations indicate CP not located forB< 200 MeV

  19. Outlook

  20. Summary With the starting of LHC (B~ 0) - we have unique opportunity to understand the properties of matter governed by quark-gluon degrees of freedom at unprecedented initial temperatures achieved in the collisions. To make the QCD phase diagram a reality equal attention needs to be given to high baryon density region. These two complementary programs will make our understanding clearer on: • characterization of quark-gluon matter at varying baryon density • finding the QCD critical point and • establishing the QCD phase boundary.

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